Limit values of the non-acyclic Reidemeister torsion for knots (Q2464802)

The Reidemeister torsion is an invariant of a CW-complex and a representation of its fundamental group. The author considers the Reidemeister torsion associated with \(\text{SL}_2(\mathbb C)\)-representations of a knot group. A bifurcation point in the \(\text{SL}_2(\mathbb C)\)-character variety of a knot group is a character which is given by both an abelian \(\text{SL}_2(\mathbb C)\)-representation and a nonabelian one. The author shows that there exist limits of the non-acyclic Reidemeister torsion at bifurcation points and the limits are expressed by using the derivation of the Alexander polynomial of the knot.